Which of the following rational number does not have a reciprocal.
(a) 1 (b) -1 (c) 0 (d) none of the above Solution: The reciprocal of a number is nothing but... View Article
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The ratio of the volume of a cylinder: volume of cone: volume of the hemisphere of same radius and same height is
(a) 1:2:3 (b) 3:1:2 (c) 1:1:1 (d) 2:3:1 Solution: Let r be radius and h be the height of the... View Article
Find the area of the following triangles.
(a) b = 4 cm, h = 3 cm (b) b = 5 cm, h = 3.2 cm (c) b... View Article
A statue, 1.6m tall, stands on the top of pedestal. From a point on the ground, the angle of elevation of the top of the statue is 600 and from the same point, the angle of elevation of the top of the pedestal is 450. Find the height of the pedestal.
(a) height of the pedestal = 0.2(√7 – 1)m (b) height of the pedestal = 0.8(√3 + 1)m (c) height... View Article
Find the value of 64-2/3.
Solution: 64-2/3 = (43)-2/3 = 4-2 = 1/42 = 1/16 Hence 64-2/3 = 1/16
Solve following equation: -x2 + x – 2 = 0
(a) (1 ± √7i)/2 (b) (-1 ± √7i)/2 (c) (2 ± √7i)/2 (d) (-2 ± √7i)/2 Solution: Given -x2 +... View Article
Solve for x: cos (sin-1 x) = 1/7
Solution: cos (sin-1 x) = 1/7 Put sin-1 x = k x = sin k x2 = sin2k => 1-x2... View Article
Estimate the sum to the nearest hundred. 458 + 324
Solution: Estimated value of 458 to nearest hundred = 500 Estimated value of 324 to nearest hundred = 300 Estimated... View Article
One root of the equation (x + 1)(x + 3)(x + 2)(x + 4) = 120 is
(A) -1 (B) 2 (C) 0 (D) 1 Solution: Given (x + 1)(x + 3)(x + 2)(x + 4) =... View Article
Fill in the blanks using the correct form of the verbs: My sister __ already __ the food.
(A) is; cooking (B) has; cooked (C) was; cooked (D) did; cooked Solution: My sister has already cooked the food.... View Article
Change the following statement into passive voice: Those who worked hard seldom obtained good marks.
(A) Good marks were seldom being obtained by those who worked hard. (B) Good marks are seldom obtained by those... View Article
If sec C is m/2√2, then m is
(a) 1 (b) 3 (c) 7 (d) none of these Solution: From the fig, triangle BDC is a right angled... View Article
There are three boys and two girls. A committee of two is to be formed. Find the probability of the event that the committee contains at least one girl.
Solution: Number of boys = 3 Number of girls = 2 Total number of people = 3+2 = 5 Find... View Article
Evaluate the following using suitable identity: 213×187
Solution: 213×187 = (200 + 13)×(200 – 13) = 2002 – 132 = 40000 – 169 = 39831 Hence 213×187... View Article
Given a metal pipe 77 cm long and inner diameter is 4 cm and outer diameter is 4.4 cm. Find the outer curved surface area of the pipe.
Solution: Height of pipe = 77 cm Outer diameter = 4.4 cm So outer radius = 2.2 cm Curved surface... View Article
If xi > 0, i = 1,2, 3, … 50 and x1 + x2 + x3 + …+x50 = 50, then the minimum value of (1/x1) + (1/x2) + ….+ (1/x50) equals
(a) 50 (b) 502 (c) 503 (d) none of these Solution: We know AM ≥ HM (x1 + x2 +... View Article
Factorise a3 – 1/a3 – 2a + 2/a.
Solution: We know a3– b3 = (a – b)(a2 + ab + b2) a3 – 1/a3 – 2a + 2/a... View Article
How many coins 1.75 cm in diameter and 2 mm thick must be melted to form a cuboid of dimensions 11 cm × 10cm × 7cm?
Solution: Diameter of coin = 1.75 cm Radius of coin = 1.75/2 cm Height = 2 mm = 0.2 cm... View Article
Find the modulus of (1+i)/(1-i) – (1-i)/(1+i).
Solution: (1+i)/(1-i) – (1-i)/(1+i) = [(1+i)(1+i) – (1-i)(1-i)]/(1+i)(1-i) = (1-1+2i – 1+ 1 + 2i)/(1+1) = 4i/2 = 2i Modulus... View Article
The mean of the cubes of the first n natural numbers is
(a) n(n+1)2/2 (b) n(n+1)2/4 (c) n2+n+1 (d) n(n+1)(n+2)/8 Solution: Sum of cubes of n natural numbers = 13 + 23... View Article
